Greatest Common Factor Calculator
Find the greatest common factor (GCD) of two integers with the full Euclidean algorithm trace, cross-checked against the lists of factors of each number. Also reports the least common multiple and whether the numbers are coprime.
TheCalculators — Greatest Common Factor Calculator
Printed thecalculators.com
GCF(24, 36)
12
24 = 2 × 12 + 0 · LCM = 72
- First number
- 24
- Second number
- 36
- GCF
- 12
- Factors of A
- 1, 2, 3, 4, 6, 8, 12, 24
- Factors of B
- 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common factors
- 1, 2, 3, 4, 6, 12
- LCM
- 72
- Coprime?
- No
Euclidean algorithm trace
The last non-zero remainder is the GCF: 12.
Step-by-step (Euclid’s algorithm)
- 1Step 124 = 0 × 36 + 24
- 2Step 236 = 1 × 24 + 12
- 3Step 324 = 2 × 12 + 0
- 4GCF foundGCF(24, 36) = 12
- 5Cross-check with factor listsLargest number appearing in both factor lists (1, 2, 3, 4, 6, 12) is 12 ✓
- 6LCM from GCFLCM = a × b ÷ GCF = 24 × 36 ÷ 12 = 72
Most useful next
Formula
GCF(a, b): repeatedly replace (a, b) with (b, a mod b) until b = 0
Pro tips
- • Euclid’s algorithm is far faster than listing factors for large numbers — usually just a handful of divisions.
- • GCF(a, b) × LCM(a, b) = a × b, so the LCM comes free once you know the GCF.
- • Coprime numbers (GCF = 1) are the reason some fractions are already in lowest terms.
FAQ
Related Calculators
More Everyday tools you might need.
Least Common Multiple Calculator
LCM of two integers via GCF, with a multiples table that shows where they first meet.
CalculateFactor Calculator
All divisors, factor pairs and prime factorization of a number, plus classification.
CalculateCommon Factor Calculator
Find all factors, common factors, GCD and LCM of two integers with Euclid steps.
CalculateFraction Calculator
Add, subtract, multiply or divide two fractions; result simplified with mixed number.
Calculate